Q. 3 Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it
take for 100 machines to make 100 toys?
This famous brain teaser — “Seven machines take 7 minutes to make 7 identical toys.
At the same rate, how many minutes would it take for 100 machines to make 100 toys?” —
tricks even math experts. With answer options (A) 1, (B) 7, (C) 100, and (D) 700,
it’s a classic test of work-rate concepts.
The Key Insight: Machine Rate per Minute
From the given information:
7 machines make 7 toys in 7 minutes.
Rate per machine:
7 toys ÷ (7 machines × 7 minutes) = 1/7 toy per minute per machine
So, one machine takes 7 minutes to make 1 toy.
This production rate remains constant. When machines and toys increase proportionally,
the time required does not change.
Correct Answer: (B) 7 Minutes
With 100 machines working at the same rate, producing 100 toys still takes:
- 7 machines → 7 toys → 7 minutes
- 100 machines → 100 toys → 7 minutes
The number of machines increases in the same proportion as the number of toys,
so the total time stays the same.
Final Answer: (B) 7 minutes
Why Other Options Are Wrong
Option (A) 1 Minute
This assumes that increasing machines automatically reduces time.
However, it ignores that producing 100 toys requires 100 times the work.
The time does not shrink below 7 minutes.
Option (C) 100 Minutes
This assumes a single machine making all toys.
It ignores the contribution of the remaining 99 machines working simultaneously.
Option (D) 700 Minutes
This multiplies toys by time per toy but forgets that 100 machines divide the work equally.
Summary Table
| Option | Time (Minutes) | Common Mistake | Why Incorrect |
|---|---|---|---|
| (A) | 1 | Over-scaling machines | Ignores total work required |
| (B) | 7 | — | Correct — constant rate |
| (C) | 100 | Single-machine assumption | Overlooks extra machines |
| (D) | 700 | Incorrect multiplication | Fails to divide work among machines |
Real-World Application: Rates in Manufacturing
This puzzle reflects real-world manufacturing and computing scenarios.
Adding machines does not always reduce time unless the workload remains constant.
It’s a popular question in aptitude tests, interviews, and competitive exams.
Mastered the “seven machines seven minutes 100 machines” puzzle?
Try more rate-based questions to sharpen your logical thinking.
